In quantum mechanics, substances are composed of electrons bound by atomic nuclei. This viewpoint is extremely powerful, and underlies modern computational approaches to electronic structure theory. These approaches—using methods like density-functional theory—are unquestionably useful, and are sufficient to provide quantitative information about energies, molecular responses, and electron distribution functions for almost all the molecules and materials of routine chemical interest. However, these computational methods and the results therefrom are in opposition to the language and concepts of chemistry. In quantum mechanics, there are no atoms, functional groups, or chemical bonds; there are no inductive effects or steric effects; there is no electronegativity or hardness; there is no electrophilicity or nucleophilicity. This makes it very challenging to gain chemical insight using modern computational quantum chemistry methods.

In this talk, I will present two examples of how chemical concepts can be deduced from quantum mechanics and, specifically, density-functional theory. For example, it is empirically known that functionalizing a molecule rarely affects the reactivity of distant sites, and it is occasionally postulated that this is due to the nearsightedness of electronic matter. We have quantified this assumption, showing that functionalization of a molecule under constant chemical potential conditions (but not under constant electron-number conditions) does not lead to changes in the electron density at far-away sites. Specifically, we have direct numerical evidence that the softness kernel is nearsighted, and that the higher-order perturbations (because alchemical transformations are not small enough to be fully described with low-order perturbation theory) are also nearsighted. Because the effects of chemical functionalization are localized, this establishes that the nearsightedness of electronic matter is the physical basis for chemical transferability. Second, I will present a mathematical argument for the “|Δμ| big is good” rule, originally proposed by Robert Parr and Weitao Yang. This rule undergirds frontier molecular orbital theory, and indicates that reagents show a tendency to prefer reaction partners so that the change in electronegativity is large. This rule subsumes many others, like the hard/soft acid/base principle and the tendency for the highest occupied molecular orbital to stabilize upon reaction.